We consider Zakharov-Kuznetsov (ZK) equation, which is a higher-dimensional version of the Korteweg-de Vries (KdV) equation, and investigate the dynamics of solutions, especially questions about the soliton stability. We first discuss the situation in two dimensions, in particular, the instability of solitons in the 2d cubic (critical) ZK equation, which leads to blow-up. Then we consider the 3d quadratic ZK equation, originally introduced by Zakharov and Kuznetsov in early 1970's, and discuss the asymptotic stability of solitons. We will also show numerical findings on the formation of solitons and radiation in this equation. This talk will be based on joint works with L.G. Farah, J. Holmer, C. Klein, N. Stoilov, K. Yang.